Question

a swimming pool is in the shape of a rectangular prism. the width is one more than five times the height, and the length is one less than eleven times the height. complete parts a and b.
a. using x for the height, write a function v(x) to represent the volume of the pool.
v(x) =
(type your answer in standard form. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Define height, width, length

Let height $h = x$.
Width $w = 5x + 1$.
Length $l = 11x - 1$.

Step2: Volume formula for prism

Volume $V(x) = l \times w \times h$

Step3: Substitute terms into formula

$V(x) = (11x - 1)(5x + 1)x$

Step4: Multiply binomials first

$(11x - 1)(5x + 1) = 55x^2 + 11x - 5x - 1 = 55x^2 + 6x - 1$

Step5: Multiply by x (height)

$V(x) = (55x^2 + 6x - 1)x = 55x^3 + 6x^2 - x$

Answer:

$V(x) = 55x^3 + 6x^2 - x$